1. Field of the Invention
This invention relates generally to the field of geophysical prospecting and, more particularly, to seismic data processing. Specifically, the invention is a method for spectral balancing of near- and far-offset seismic data.
2. Description of the Related Art
Amplitude versus offset (AVO) is a seismic data analysis method based on studying the variation in the amplitude of reflected waves with changes in the distance (offset) between the seismic source and receiver. The AVO response of the reflection events associated with the boundaries between the reservoir rock and the surrounding sealing materials often depends on the properties of the fluid stored in the reservoir pore space. Because of this property, AVO analysis is often used as a tool for reservoir fluid prediction.
A common difficulty for AVO analysis is that the frequency spectra of near- and far-offset data are different. In general, near-offset sections contain more high-frequency energy than far-offset sections. This variation in frequency content can significantly alter the AVO response, since the interference patterns between adjacent reflection events (for instance the top and bottom of a layer) will be different on the near- and far-offset data. Difference in interference (tuning) can create false AVO anomalies or make valid AVO anomalies disappear. Because of their different frequency spectra, correlating reflection events between near- and far-offset sections is often impossible or ambiguous.
FIG. 1 shows an example of a change in frequency spectra between near- and far-offset sections. The near-offset section 101, on the left half of the figure, contains a larger number of cycles than the far-offset section 102, on the right half of the figure. Analysis of the AVO response of a given cycle is impossible when the cycle is not present in both near- and far-offset sections. FIG. 2 illustrates a similar situation with a Common-Depth-Point (CDP) gather. There are several cycles in the near offsets 201, on the left half of the figure, that get lost, or coalesce with other cycles, in moving along the section towards the far offsets 202, on the right half of the figure. Two areas where cycles are lost are indicted by reference numbers 203 and 204. These examples illustrate the need for a method of balancing the spectra of near- and far-offset data before AVO analysis.
A number of publications have dealt with the different effects that distort AVO measurements. Perhaps the most complete listing of such effects was given by Duren, R. E., 1991, xe2x80x9cSeismic range equationxe2x80x9d, Geophysics, 56, 1015-1026, who developed the seismic range equation to account and correct for the effects of source and receiver array directivity, waveform spreading, and losses due to transmission, interbed multiples and attenuation (Q). Yet Duren ignored the effect of Normal Moveout (NMO) stretch, also known as offset-dependent tuning. The distortion in NMO stretch is caused by the fact that arrival time differences between reflection events change as a function of offset. Since the timing relationships between different events change, the corresponding interference patterns between reflection events also change, and this has a large effect on the reflection amplitudes.
Several authors recognized the significance of NMO stretch on AVO measurements and suggested methods to compensate for it. Three different approaches for correcting the AVO intercept and gradient for the effect of NMO stretch are described by (1) Corcoran, C. T., Leveille, J. P., and Velasco, E. S., 1991, xe2x80x9cMethod for processing seismic dataxe2x80x9d, U.S. Pat. No. 4,995,007; (2) Swan, H. W., 1997, xe2x80x9cRemoval of offset-dependent tuning in AVO analysisxe2x80x9d, Expanded abstracts of 67th Ann. Int. SEG Mtg., 175-178; and (3) Dong, W., 1999, xe2x80x9cAVO detectability against tuning and stretching artifactsxe2x80x9d, Geophysics, 64, 494-503. All three of these approaches rely on a model for the amplitude of the reflect ions as a function of offset, expressed by the equation:
S(t,xcex8)=A(t)+B(t)sin2(xcex8).
Here S (t, xcex8) is the amplitude of a reflection at time t (after NMO) for a reflection angle xcex8, A(t) is a time series usually called the intercept, and B(t) is another time series called the gradient.
AVO analysis is often accomplished by perform in g a leas t-squares fit of the NMO-corrected data and estimating A(t) and B(t), which are further studied to indicate th e presence or absence of hydrocarbons in the layers that generate the reflections. NMO stretch causes significant distortions of the intercept and gradient time series A(t) and B(t). The three authors mentioned above presented different methods for correcting those distorted intercept and gradient series for the effect of NMO stretch. The main shortcoming of the above approaches is that they can only be used after the intercept and gradient have been calculated. Generally, the intercept and gradient calculations are extremely sensitive to small misalignments of the near- and far-offset data, caused by slightly inaccurate NMO velocities. These misalignments produce distortions of A(t) and B(t) that are often much larger than those caused by NMO stretch. Because of this, it is very desirable for practical AVO applications to be able to correct the data for the effect of NMO stretch without having to first estimate the intercept and gradient time series.
Castoro, A., 1998, xe2x80x9cMapping reservoir properties through prestack seismic attribute analysisxe2x80x9d, Chapter 5: Offset dependent tuning, 130-157, Ph.D. thesis, Research School of Geological and Geophysical Sciences, Birkbeck College, University of London, describes a method for correcting for NMO stretch without first estimating the intercept and gradient time series. Yet, Castoro""s approach can only be applied to target zones and not to the whole trace. This is a significant shortcoming, since AVO analysis is often applied to large 3-D seismic cubes as a reconnaissance tool.
Wapenaar, K., Van der Leij, T., Van Geloven, W., Van Wijngaarden, A. J., 1996, xe2x80x9cCompensating for the effects of fine-layering on AVA (Amplitude Vs. Angle)xe2x80x9d, Extended abstracts of 58th EAGE conference, vol.1, paper no. C035, proposes a seismic migration (imaging) algorithm that can correct for the effect of NMO stretch. Yet, typically AVO analysis is performed on data that have already been migrated (imaged) with a variety of migration algorithms. Hence, it is desirable to have an NMO stretch compensation method that is independent of the choice of migration algorithm.
The application of NMO stretch compensation to the data can be detrimental for AVO analysis if it is not accompanied by a compensation for the frequency-dependent losses that also affect the data. This is an additional consideration that is not addressed by any of the previous authors. Therefore, it is desirable that, if NMO stretch compensation is applied, amplitude losses caused by frequency-dependent mechanisms are also compensated for. Such mechanisms tend to affect higher-frequency energy more than lower-frequency energy.
An important frequency-dependent loss mechanism is the absorption of the wave energy by transformation to heat that causes attenuation of the wave amplitudes. Standard absorption-compensation methods attempt to compensate for all absorption losses since the waves entered the subsurface. Such methods often have detrimental effects on data quality, because they amplify high-frequency noise. It is thus desirable to have an approach for absorption compensation for AVO applications that is applicable to the whole trace and corrects for the relative amplitude loss between the near- and far-offset data.
Thus, there exists a need for a method to compensate for the effects of both NMO stretch and frequency-dependent loss mechanisms such as absorption on seismic data for AVO analysis that can be applied to whole traces, that is independent of the choice of migration algorithm, that does not require estimates of the intercept and gradient time series, and that corrects for the relative amplitude loss between the near- and far-offset data.
The invention is a method for spectral balancing of near- and far-offset seismic data. Initially, velocity and offsets are determined for the seismic data. Then two compensation filters are created. First, an NMO stretch compensation filter is created by the following steps. A frequency spectrum of the near-offset seismic data is estimated and a stretch factor xcex2 is calculated for the frequency spectrum, using the velocity and the offsets. A stretched frequency spectrum of near-offset seismic data is calculated, based on the stretch factor xcex2. The frequency spectrum of near-offset seismic data is divided by the stretched frequency spectrum of near-offset seismic data, generating a first frequency response filter. High frequency gain is limited in the first frequency response filter, generating a first gain-limited filter. The first gain-limited filter is convolved with a low pass filter, generating the NMO stretch compensation filter. Then the NMO stretch compensation filter is applied to the seismic data. Second, a relative Q compensation filter is created by the following steps. A difference in amplitude loss between the near- and far-offset seismic data is calculated, using the velocity and the offsets. A frequency gain is calculated, based on the difference in amplitude loss. A second frequency response filter is created, based on the frequency gain. High frequency gain is limited in the second frequency response filter, generating a second gain-limited filter. The second gain-limited filter is convolved with a low pass filter, generating the relative Q compensation filter. The relative Q compensation filter is applied to the seismic data.